scholarly journals Optimal reinsurance: a reinsurer’s perspective

2017 ◽  
Vol 12 (1) ◽  
pp. 147-184 ◽  
Author(s):  
Fei Huang ◽  
Honglin Yu
Keyword(s):  
At Risk ◽  
Closed Form ◽  
Value At Risk ◽  
Optimality Criteria ◽  
Total Loss ◽  
Optimal Reinsurance ◽  
Numerical Examples ◽  
Dependency Structure ◽  
Closed Form Solutions

AbstractIn this paper, the optimal safety loading that the reinsurer should set in the reinsurance pricing is studied, which is novel in the literature. It is first assumed that the insurer will choose the form of the reinsurance contract by following the results derived in Cai et al. Different optimality criteria from the reinsurer’s perspective are then studied, such as maximising the expectation of the profit, maximising the utility of the profit and minimising the value-at-risk of the reinsurer’s total loss. By applying the concept of comonotonicity, the problem in which the reinsurer is facing two risks with unknown dependency structure is also solved. Closed-form solutions are obtained when the underlying losses are zero-modified exponentially distributed. Finally, numerical examples are provided to illustrate the results derived.

scholarly journals Optimal Limited Stop-Loss Reinsurance under VaR, TVaR, and CTE Risk Measures

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Xianhua Zhou ◽  
Huadong Zhang ◽  
Qingquan Fan
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Loss Ratio ◽  
Optimal Reinsurance ◽  
Numerical Examples ◽  
Optimal Values ◽  
Stop Loss ◽  
Conditional Tail Expectation ◽  
Reinsurance Market

This paper aims to provide a practical optimal reinsurance scheme under particular conditions, with the goal of minimizing total insurer risk. Excess of loss reinsurance is an essential part of the reinsurance market, but the concept of stop-loss reinsurance tends to be unpopular. We study the purchase arrangement of optimal reinsurance, under which the liability of reinsurers is limited by the excess of loss ratio, in order to generate a reinsurance scheme that is closer to reality. We explore the optimization of limited stop-loss reinsurance under three risk measures: value at risk (VaR), tail value at risk (TVaR), and conditional tail expectation (CTE). We analyze the topic from the following aspects: (1) finding the optimal franchise point with limited stop-loss coverage, (2) finding the optimal limited stop-loss coverage within a certain franchise point, and (3) finding the optimal franchise point with limited stop-loss coverage. We provide several numerical examples. Our results show the existence of optimal values and locations under the various constraint conditions.

On the closed form solutions for non-extensive Value at Risk

2009 ◽  
Vol 388 (17) ◽  
pp. 3536-3542 ◽  
Author(s):  
S. Stavroyiannis ◽  
I. Makris ◽  
V. Nikolaidis
Keyword(s):  
At Risk ◽  
Closed Form ◽  
Value At Risk ◽  
Closed Form Solutions

Elastic Fields in a Polygon-Shaped Inclusion With Uniform Eigenstrains

1997 ◽  
Vol 64 (3) ◽  
pp. 495-502 ◽  
Author(s):  
H. Nozaki ◽  
M. Taya
Keyword(s):  
Composite Materials ◽  
Closed Form ◽  
Strain Field ◽  
Strain Energy ◽  
Convex Polygon ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Closed Form Solutions ◽  
Arbitrary Convex ◽  
Shaped Inclusion

In this paper the elastic fields in an arbitrary, convex polygon-shaped inclusion with uniform eigenstrains are investigated under the condition of plane strain. Closed-form solutions are obtained for the elastic fields in a polygon-shaped inclusion. The applications to the evaluation of the effective elastic properties of composite materials with polygon-shaped reinforcements are also investigated for both dilute and dense systems. Numerical examples are presented for the strain field, strain energy, and stiffness of the composites with polygon shaped fibers. The results are also compared with some existing solutions.

Optimal Reciprocal Reinsurance under VaR or TVaR Constraint

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hung-Hsi Huang ◽  
Ching-Ping Wang
Keyword(s):  
At Risk ◽  
Risk Management ◽  
Moral Hazard ◽  
Value At Risk ◽  
Incentive Compatibility ◽  
Regular Form ◽  
Optimal Reinsurance ◽  
The Common ◽  
Risk Constraint ◽  
Management Requirement

Abstract Most existing researches on optimal reinsurance contract are based on an insurer’s viewpoint. However, the optimal reinsurance contract for an insurer is not necessarily to be optimal for a reinsurer. Hence, this study aims to develop the optimal reciprocal reinsurance which satisfies the benefits of both the insurer and reinsurer. Additionally, due to legislative restriction or risk management requirement, the wealth of insurer and reinsurer are frequently imposed upon a VaR (Value-at-Risk) or TVaR (Tail Value-at-Risk) constraint. Therefore, this study develops an optimal reciprocal reinsurance contract which maximizes the common benefits (evaluated by weighted addition of expected utilities) of the insurer and reinsurer subject to their VaR or TVaR constraints. Furthermore, for avoiding moral hazard problem, the developed contract is additionally restricted to a regular form or incentive compatibility (both indemnity schedule and retained loss schedule are continuously nondecreasing).

scholarly journals A consistent estimator to the orthant-based tail value-at-risk

2018 ◽  
Vol 22 ◽  
pp. 163-177 ◽  
Author(s):  
Nicholas Beck ◽  
Mélina Mailhot
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Arbitrary Dimension ◽  
Real Data ◽  
Consistent Estimator ◽  
Numerical Examples ◽  
Theoretical Results

In this paper, we address the estimation of multivariate value-at-risk (VaR) and tail value-at-risk (TVaR). We recall definitions for the bivariate lower and upper orthant VaR and bivariate lower and upper orthant TVaR, presented in Cossette et al. [Eur. Actuar. J. 3 (2013) 321–357 or Methodol. Comput. Appl. Probab. (2014) 1–22]. Here, we present estimators for both these measures extended to an arbitrary dimension d ≥ 2 and establish the consistency of our estimator for the lower and upper orthant TVaR in any dimension. We demonstrate these results by providing numerical examples that compare our estimator to theoretical results for both simulated and real data.

scholarly journals Reliability of Sampling Inspection Schemes Applied to Replacement Steam Generators

2006 ◽  
Vol 129 (1) ◽  
pp. 109-117 ◽  
Author(s):  
Guy Roussel ◽  
Leon Cizelj
Keyword(s):  
Closed Form ◽  
Steam Generator ◽  
The State ◽  
The Other ◽  
Prior Density ◽  
Steam Generators ◽  
Numerical Examples ◽  
Closed Form Solutions ◽  
Sampling Inspection ◽  
Steam Generator Tubing

The basis for determining the size of the random sample of tubes to be inspected in replacement steam generators is revisited in this paper. A procedure to estimate the maximum number of defective tubes left in the steam generator after no defective tubes have been detected in the randomly selected inspection sample is proposed. A Bayesian estimation is used to obtain closed-form solutions for uniform, triangular, and binomial prior densities describing the number of failed tubes in steam generators. It is shown that the particular way of selecting the random inspection sample (e.g., one sample from both SG, one sample from each SG, etc.) does not affect the results of the inspection and also the information obtained about the state of the uninspected tubing, as long as the inspected steam generators belong to the same population. Numerical examples further demonstrate two possible states of the knowledge existing before the inspection of the tubing. First, virtually no knowledge about the state of the steam generator tubing before the inspection is modeled using uniform and triangular prior densities. It is shown that the knowledge about the uninspected part of the tubing strongly depends on the size of the sample inspected. Further, even small inspection samples may significantly improve our knowledge about the uninspected part. On the other hand, rather strong belief on the state of the tubing prior to the inspection is modeled using binomial prior density. In this case, the knowledge about the uninspected part of the tubing is virtually independent on the size of the sample. Furthermore, it is shown qualitatively and quantitatively that such inspection brings no additional knowledge on the uninspected part of the tubing.

Estimating and Predicting Value-at-Risk in the presence of structural breaks: A Study based on unbiased extreme value volatility estimator

2020 ◽  
Vol 14 (1) ◽  
pp. 27-48
Author(s):  
Dilip Kumar
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Structural Breaks ◽  
Extreme Value ◽  
Total Loss ◽  
Fat Tails ◽  
Alternative Models ◽  
Forecasting Performance ◽  
The Impact ◽  
The Given

We provide a framework based on the unbiased extreme value volatility estimator to predict long and short position value-at-risk (VaR). The given framework incorporates the impact of asymmetry, structural breaks and fat tails in volatility. We generate forecasts of both long and short position VaR and evaluate the VaR forecasting performance of the proposed framework using various backtesting approaches for both long and short positions and compare the results with that of various alternative models. Our findings indicate that the proposed framework outperforms the alternative models in predicting the long and the short position VaR. Our findings also indicate that the VaR forecasts based on the proposed framework provides the least total loss score for various long and short positions VaR and this supports the superior properties of the proposed framework in forecasting VaR more accurately. The study contributes by providing a framework to predict more accurate VaR measure based on the unbiased extreme value volatility estimator.

scholarly journals Solving Nonlinear Differential Algebraic Equations by an Implicit Lie-Group Method

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Chein-Shan Liu
Keyword(s):  
Closed Form ◽  
Lie Group ◽  
Iterative Scheme ◽  
Differential Algebraic Equations ◽  
Group Method ◽  
Computational Results ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Closed Form Solutions ◽  
Lie Group Method

We derive an implicit Lie-group algorithm together with the Newton iterative scheme to solve nonlinear differential algebraic equations. Four numerical examples are given to evaluate the efficiency and accuracy of the new method when comparing the computational results with the closed-form solutions.

Closed-form approximations for operational value-at-risk

2013 ◽  
Vol 8 (4) ◽  
pp. 39-54 ◽  
Author(s):  
Lorenzo Hernández ◽  
Jorge Tejero ◽  
Alberto Suárez ◽  
Santiago Carrillo-Menéndez
Keyword(s):  
At Risk ◽  
Closed Form ◽  
Value At Risk
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